Can I hook my TINI up directly to the 10BaseT port on my PC, or do I have to go through a hub?

Yes, you can hook your TINI directly to a PC without using a hub,
as long as you have a 10BaseT-capable Ethernet card installed
in your PC.
But you must use a special type of 10BaseT cable known as a
crossover cable. A crossover cable has the transmit
and receive lines crossed internally so that the transmit pins on one end are connected to the receive pins on the other.

The pinouts of both a crossover cable and a "normal", or straight-through, cable are as follows:

where NC stands for "Not Connected". Pin 1 is
on the right hand side of the RJ-45 plug if you look at the end
of the cable with the latch pointing down. Likewise, Pin 1
is on the left hand side of the RJ-45 jack if you look into the
jack with the notch on the bottom.

It's always a good idea to verify that you are using the correct type
of cable. You can do this visually (most 10BaseT cables have
color-coded strands which can be seen through the clear plastic
of the plug) or electrically, by mesuring resistance.

As a final note, you might also have to set a jumper on your Ethernet card if you have a 10/100BaseT card that doesn't autosense the speed.
However, this isn't the norm.